This happens pretty regularly in the UK. A detectorist finds a group of coins, the UK determines the museums don't need them since they aren't very important, but some local group wishes to keep them. Good for them if they wish to raise the money. The UK has the best system in the world for ensuring the detectorist gets compensated, the nation can keep its important finds, and even local groups get a chance to retain local heritage. I simply cannot grasp how the rest of the world doesn't see how ingenious and wonderful the UK's laws are in this regard. History, science, land owners, museums, and coin collectors ALL would be better off if every nation followed the UK's lead. Hats off to all UK members for having a brilliant law.
Unlikely to happen for a variety of reasons, but while you refer to the UK here, those laws do not even apply to the UK. It's basically England and Wales (not sure about Northern Ireland) but not Scotland ... (Edit: ... as the link in green18's post shows. Should have checked that out before. ) Christian